IMAGE-RECONSTRUCTION USING A GENERALIZED NATURAL PIXEL BASIS

The solution q of the imaging equation Mq=FGq=p (F is the projector an d G is a generalized backprojector) is determined using least squares, thus various basis functions can be used as an expansion for the reco nstructed image. In this paper a generalized natural pixel basis is ch osen to allow flexibility in formulating the vector space for the solu tion q. The singular value decomposition (SVD) method is used to solve for q, and the final image is obtained by backprojecting q: p = Gq, a nd sampling p at a discrete array of points. Truncated parallel and no n-truncated fan beam projection measurements were used to demonstrate that the solution q to Mq=FGq=p can be defined wherein, for example, i f F is a fan beam projection operator, G can be a parallel backproject ion operator defined based upon natural pixels. It is demonstrated tha t different backprojection geometries can give almost equivalent recon structions of non-truncated projections. For truncated projections the estimation of q that covers the entire projection of the object is ef fective in reducing ring artifacts; however, using more projection bin s is much more effective in preserving the resolution than is increasi ng the projection bin width. Also, a generalized natural pixel basis b etter models the geometric response of a collimator used in SPECT, the refore reconstructions of fan beam projections using generalized natur al pixels are shown to have better resolution than those that use the filtered backprojection algorithm.